Discussiones Mathematicae Graph Theory 27(1) (2007) 39-44
doi: 10.7151/dmgt.1342

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A NOTE ON UNIQUELY H-COLOURABLE GRAPHS

Anthony Bonato

Department of Mathematics
Wilfrid Laurier University
Waterloo, ON, Canada, N2L 3C5
e-mail: abonato@rogers.com

Abstract

For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.

Keywords: graph homomorphisms, core graphs, uniquely H-colourable.

2000 Mathematics Subject Classification: 05C15, 05C75.

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Received 20 June 2005
Revised 22 May 2006